Solve H=1/frac{1{5}+1/10+1/15+1/20+frac{1}{25}}

$$H = \frac { 1 } { \frac { 1 } { 5 } + \frac { 1 } { 10 } + \frac { 1 } { 15 } + \frac { 1 } { 20 } + \frac { 1 } { 25 } }$$

Solve for H

$$H = \frac{300}{137} = 2\frac{26}{137} \approx 2.189781022$$

Steps for Solving Linear Equation

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{1}{10} to fractions with denominator 10.

$$H=\frac{1}{\frac{2}{10}+\frac{1}{10}+\frac{1}{15}+\frac{1}{20}+\frac{1}{25}}$$

Since \frac{2}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$H=\frac{1}{\frac{2+1}{10}+\frac{1}{15}+\frac{1}{20}+\frac{1}{25}}$$

Add 2 and 1 to get 3.

$$H=\frac{1}{\frac{3}{10}+\frac{1}{15}+\frac{1}{20}+\frac{1}{25}}$$

Least common multiple of 10 and 15 is 30. Convert \frac{3}{10} and \frac{1}{15} to fractions with denominator 30.

$$H=\frac{1}{\frac{9}{30}+\frac{2}{30}+\frac{1}{20}+\frac{1}{25}}$$

Since \frac{9}{30} and \frac{2}{30} have the same denominator, add them by adding their numerators.

$$H=\frac{1}{\frac{9+2}{30}+\frac{1}{20}+\frac{1}{25}}$$

Add 9 and 2 to get 11.

$$H=\frac{1}{\frac{11}{30}+\frac{1}{20}+\frac{1}{25}}$$

Least common multiple of 30 and 20 is 60. Convert \frac{11}{30} and \frac{1}{20} to fractions with denominator 60.

$$H=\frac{1}{\frac{22}{60}+\frac{3}{60}+\frac{1}{25}}$$

Since \frac{22}{60} and \frac{3}{60} have the same denominator, add them by adding their numerators.

$$H=\frac{1}{\frac{22+3}{60}+\frac{1}{25}}$$

Add 22 and 3 to get 25.

$$H=\frac{1}{\frac{25}{60}+\frac{1}{25}}$$

Reduce the fraction \frac{25}{60} to lowest terms by extracting and canceling out 5.

$$H=\frac{1}{\frac{5}{12}+\frac{1}{25}}$$

Least common multiple of 12 and 25 is 300. Convert \frac{5}{12} and \frac{1}{25} to fractions with denominator 300.

$$H=\frac{1}{\frac{125}{300}+\frac{12}{300}}$$

Since \frac{125}{300} and \frac{12}{300} have the same denominator, add them by adding their numerators.

$$H=\frac{1}{\frac{125+12}{300}}$$

Add 125 and 12 to get 137.

$$H=\frac{1}{\frac{137}{300}}$$

Divide 1 by \frac{137}{300} by multiplying 1 by the reciprocal of \frac{137}{300}.

$$H=1\times \frac{300}{137}$$

Multiply 1 and \frac{300}{137} to get \frac{300}{137}.

$$H=\frac{300}{137}$$

Assign H

$$H≔\frac{300}{137}$$